Design News, May 2013

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AU TIVE MO M E S IC A ES D L Control Electronics Digital Control Systems mechatronics Mechanical CAD Electronic Systems Electromechanics SE TU RI NG Software RAPHY ROG XE S M FA Y E C Mechanical Systems S T U M AT E R I ALS PR OC CE Control Systems N FE DE MECHATRONICS IN DESIGN AERO SP A G I N TO M S CO A N S CT NSU MER PRODU Frequency Response— The Gold Standard Engineers predict real-world response and identify model parameters. WHAT DO ENGINEERS, "see" when they look at a real system or when they conceive a new design? They will look past the hardware and visualize the flow of energy, where it is stored, and where it is dissipated. They will identify the kinetic energy of moving fluids and solid masses; the potential energy of compressible fluids, elastic hoses and tanks, and deformable solids; the energy stored in electric and magnetic fields; and the energy lost through friction generating heat. But they will also "see" how the system might respond to real-world inputs by understanding the frequency response of the system and the frequency spectrum of the probable inputs. A real system often can be modeled, over some range of motion and time duration, as a stable, linear, phases of these sine waves, time-invariant system. If the one can generate a waveinput to this system is a sine form identical to the desired wave, the steady-state outsignal. A periodic function put (after the transients have qi(t) can be represented by died out) is also a sine wave an infinite series of terms with the same frequency, but called a Fourier series. The with an amplitude and phase figures show a square wave angle that are both frequen- Kevin C. Craig, Ph.D., and a plot of the first few cy-dependent. Plots of the Robert C. Greenheck terms of the Fourier series. input-output amplitude ratio Chair in Engineering The more terms used in the vs. frequency and the phase Design & Professor of series, the better the fit. angle vs. frequency are called Mechanical EngineerUsing the principle of ing, College of Engithe Bode plots. If the system neering, Marquette superposition for linear sysbeing excited were a nonlin- University. tems, we can combine the ear or time-varying system, frequency spectrum of a the output might contain frequencies real-world signal with the system's freother than the input frequency and the quency response and calculate the sysamplitude ratio might be dependent on tem time response. The device used to the input magnitude. Any real-world de- experimentally determine a system's vice or process will only need to function frequency response is called a dynamproperly for a certain range of frequen- ic signal analyzer (DSA) and there are cies; outside this range we don't care what many excellent application notes availhappens. When one has the frequency- able on its use. response curves for any system and is Frequency response testing plays given a specific sinusoidal input, it is an a most significant role in grey-box easy calculation to get the sinusoidal out- modeling, discussed here last month. put. What is not obvious, but extremely For example, once one has the model important, is that the frequency-response structure for a device, such as a solecurves are really a complete description noid-operated proportional valve used of the system's dynamic behavior and in fluid power applications, the meaallow one to compute the response for sured frequency-response data can be any input, not just sine waves. used with optimization algorithms to Two hundred years ago, Jean Bap- determine the model parameters. And tiste Fourier showed that any periodic we all know that a model is worth a waveform that exists in nature can be thousand tests! This exact situation generated by adding up sine waves. By is presented by The MathWorks at picking the amplitudes, frequencies, and DN Design News | MAY 2013 | w w w. d e s i g n n e w s . c o m –24– magenta cyan yellow black ES245921_DN1305_024.pgs 05.03.2013 05:04 UBM

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